A thermodynamically consistent phase-field-micromechanics model of sintering with coupled diffusion and grain motion

Abstract

Sintering is crucial for processing ceramic and metallic powders into solid objects, and understanding microstructure evolution is essential for manufacturing tailored products. While various phase-field models have been proposed to simulate microstructure evolution in solid-state sintering, correctly incorporating the crucial grain-motion-induced densification mechanism remains challenging. This issue stems from an ad hoc treatment of the micromechanics of grain motion, where the thermodynamical driving force is not derived from the system's free energy. This study introduces a novel phase-field-micromechanics model of sintering (PFMMS) that addresses this long-standing challenge. The PFMMS defines a unified energy law, deriving governing equations using variational principles, ensuring thermodynamic consistency. The driving force for grain motion is derived from the system's free energy, eliminating non-densifying phenomena that may occur in existing models and ensuring energy reduction. This approach represents a significant advancement over our previous work, which was experimentally validated. The PFMMS is verified against theoretical and numerical benchmarks, capturing intrinsic stress distribution and system-size-independent shrinkage strain while maintaining thermodynamic equilibrium states. These results meet essential requirements for a consistent and reliable sintering model, offering potential applications in the manufacturing of high-performance ceramics and metals with precisely controlled microstructures.